1. Topology of the protein network H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)

2. Erdös-Rényi model (1960) - Democratic - Random Pál Erdös Pál Erdös (1913-1996) Connect with probability p p=1/6 N=10  k  ~ 1.5

3. Degree distribution of a random graph P(k): the probability that a node has k links P(k)= C k N-1 p k (1-p) N-1-k For large N P(k) can be replaced by a Poisson distribution: P(k)~ e - k /k! Poisson distribution

4. World Wide Web Over 3 billion documents ROBOT: collects all URL’s found in a document and follows them recursively Nodes: WWW documents Links: URL links R. Albert, H. Jeong, A-L Barabasi, Nature, 401 130 (1999). WWW Expected P(k) ~ k -  Found Scale-free Network Exponential Network

5. Scale-free model Barabási & Albert, Science 286, 509 (1999) P(k) ~k -3 (1) Networks continuously expand by the addition of new nodes WWW : addition of new documents Citation : publication of new papers GROWTH: add a new node with m links PREFERENTIAL ATTACHMENT: the probability that a node connects to a node with k links is proportional to k. (2) New nodes prefer to link to highly connected nodes. WWW : linking to well known sites Citation : citing again highly cited papers

6. Other Models

7. Internet

8. Metabolic network Organisms from all three domains of life are scale-free networks! H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 407 651 (2000) ArchaeaBacteriaEukaryotes

9. http://www.orgnet.com

11. Many real world networks have a similar architecture: Scale-free networks WWW, Internet (routers and domains), electronic circuits, computer software, movie actors, coauthorship networks, sexual web, instant messaging, email web, citations, phone calls, metabolic, protein interaction, protein domains, brain function web, linguistic networks, comic book characters, international trade, bank system, encryption trust net, energy landscapes, earthquakes, astrophysical network…

12. Copyright ©2002 American Society for Biochemistry and Molecular Biology Deane, C. M. (2002) Mol. Cell. Proteomics 1: 349-356 Interacting yeast proteins as detected in several studies

13. L.Salwinski & D.Eisenberg. Curr.Op.Struct.Biol. 13 (2003)

14. J.S. Bader et al.. Nature Biotechnology 22 (2004)

15. Filtered Yeast Interactome dataset (Han et al., Nature 430, 2004) (HT-Y2H) projects (5,249 potential interactions - union of the available data sets) Co-IP (6,630 potential interactions from two datasets) in silico computational predictions of interactions (7,446 potential interactions from the 'von Mering' data set obtained from the union of gene co-occurrence, gene neighbourhood and gene fusion predictions) 'MIPS protein complexes' published singly in the literature (9,597 pairwise interactions between components of complexes MIPS physical interactions (excluding genome-scale experiments: 1,285 interactions).

16. J-D. Han et al. Nature 430 (2004)

17. UNIPROT DATABASE filtered by SEG UNIPROT DATABASE filtered by SEG VirusesBacteriaArchaeaAscomycotaMetazoaSpermatophyta

18. BLASTP S. Cerevisiae sequence as a query BACTERIA METAZOA VIRUSES 10 -4 1 ARCHAEA Top scoring sequences from each group  parwise SW homology check with 100 randomisations and Z-score cutoff

19. A-L. Barabasi & Z.N. Oltvai. Nature Reviews Genetics 5 (2004)

21. Archaea, Eubacteria, Fungi, Plants, Animals (33/26)  protein synthesis machinery (40S and 60S ribosomal subunits, translational factors, t-RNA synthetases  basic metabolism (e.g. ATP synthesis, Krebs cycle)  protein folding and degradation (chaperones, proteases)  domains participating in protein-protein interactions (TPR, WD40)  +Viruses (16/5)  replication (RNA polymerases, helicases, replication factor C, ribonucleotide reductase)  protein degradation (19S proteasome)

22. 40S ribosome Mitochondrial ribosomal 40S subunit

23. S. Wuchty, Z.N. Oltvai & A-L. Barabasi. Nature Genetics 22 (2003)

24. Mitochondrial alpha-ketoglutarate dehydrogenase and pyruvate degydrogenase complexes Succinate dehydrogenase

25. General repressor of transcription Coatomer Nuclear pore Nuclear pore Anaphase-promoting complex (ubiquitin-protein ligase) Cyclophilin, heat shock protein (HSP82) and STI1 inhibitor

26. Eubacteria, Eukaryota |Archaea (4/4) Eubacteria, Eukaryota |Archaea (4/4)  catalytic core delta subunit of mitochondrial ATP-ase  tubulin (BtubA/B - Prosthecobacter  tubulin (BtubA/B - Prosthecobacter )  mitochondrial subunits of 60S ribosome  RNA-binding proteins (cleavage factor I)

27. Mitochondrial ribosomal proteins of the 60S subunit Central stalk of mitochondrial F1F0 ATP synthase Subunits of cleavage factor I (HRP1, RNA15), poly-A binding protein (PAB1, SGN1), uncharacterized protein YGR250C Alpha- and beta-tubulin

28. Archaea, Eukaryota | Eubacteria (8/8)  RNA polymerase II (non-catalytic subunits)  60S ribosomal subunits (cytoplasmatic)  splicing (archeal-like LSM proteins)  exosome 3’  5’ exoribonuclease complex  20S proteasome

29. Protein components of large 60S ribosome subunit Subunits of RNA polymerase II

30. Eukaryota | Archaea, Eubacteria, Viruses (24/19)  vesicle transport and membrane fusion (multicompartmental cell)  mitochondrial transporters  regulation of actin cytoskeleton stability

31. Actin cytoskeleton regulating complex Actin capping heterodimer Cofilin like protein and adenylyl cyclase-asssociated protein

32. Mitochondrial inner membrane ATP/ADP translocator and mitochondrial inner membrane transporters (TIM22, TIM9, MRS1) Mitochondrial transport system

33. M.C. Rivera & J.A.Lake Nature 431 (2004)

34. M.C. Rivera & J.A.Lake Nature 431 (2004) M.C. Rivera & J.A.Lake Nature 431 (2004)

35. M.C. Rivera & J.A. Lake Nature 431 (2004) 4248 49

36. L.Giot et al. Science. 2003, 302 (2003)

37. Subunits of 26 S proteasome comlex

38. Trehalose-6-phosphate complex

39. PL GPL+EC The number of S. cerevisiae proteins The node degree

40. Linear combination of exponential decays method: „S” „F”

41. DEL

42. The contribution of “F” and “S” component

44. PL GPL+EC DEL AICc = 94.6 AICc = 135.8 AICc = 112.4

45. Akaike's Information Criterion (AICc) - the average squared residual for a given model, m - the number of the model parameters, z - the number of observations

46. Interacting proteins